Heavy compares the flop card to the way a fake body is dropped by the Spy's feign-death device: The Dead Ringer.
Several times Heavy mentions Sandviches. In particular, his comment about becoming an unstoppable killing machine is a reference to the video Meet the Sandvich, where, after eating a Sandvich, the Heavy punches all of the BLU Scout's blood out and breaks the BLU Soldier's spine.
If the player is idle for too long, Heavy may say that the player is like a sleeping soldier who just stands in his/her base instead of running to the point. This may be a reference to players who idle in their spawnrooms in order to get items without actually playing.
Heavy's fear of ghosts is a reference to the Halloween events in Team Fortress 2 where a ghost or the Horsless Headless Horseman appear, who can put all classes into a helpless fleeing state.